Consider the following two principles, the Identity of Indiscernibles and Indiscernability of Identicals.
For any property F, if object x has F just in case y has F, then x = y.
For any objects x and y, if x = y, then x has F just in case x has F.
The second principle is trivial but the first is not. Could an object x and an object y has all of the same intrinsic and extrinsic properties and yet be distinct? Consider the following argument that the Identity of Indiscernibles is false.
- Suppose the universe contains two perfectly symmetric iron spheres two miles apart which have all the same intrinsic and relational properties and there is nothing else.
- It follows that the two spheres possess the same properties and hence are indistinguishable.
- However, they are not identical.
- Hence, indiscernibles may not be identical.
Question: Do you agree with the premises? If not, which premise(s) do you reject?